Analytic semigroups on \(L_\omega^p(0,1)\) and on \(L^p(0,1)\) generated by some classes of second order differential operators (Q1304460)

Given \(\alpha\in C[0,1]\) with \(\alpha>0\) in \((0,1)\), \(\alpha(0)= \alpha(1)= 0\), and \(\beta\) a real-valued function in \(L^\infty(0,1)\), the authors consider the degenerate differential operator \[ Au:= \alpha u''+\beta u' \] and prove that under regularity (and compatibility) assumptions on the coefficients \(\alpha\) and \(\beta\) the operator \(A\) restricted to suitable domains can generate an analytic semigroup on \(L^p[0,1]\), \(1<p<\infty\).